Smoothing Splines Approximation Using Hilbert Curve Basis Selection

• DOI: 10.1080/10618600.2021.2002161
• Publication Date: 2021-11-08T16:56:40Z
• Authors: Cheng Meng; Jun Yu; Yongkai Chen; Wenxuan Zhong; Ping Ma
• Keywords: Smoothing; Basis function; Basis (linear algebra); Spline (mechanical)

Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing is significant when sample size n large. When number predictors d ≥ 2 , cost for at order O(n3) using standard approach. Many methods developed to approximate spline estimators by q basis functions instead ones, resulting a O(nq2). These are called selection methods. Despite algorithmic benefits, most require assumption that uniformly-distributed on hyper-cube. may deteriorating performance such an not met. To overcome obstacle, we develop efficient algorithm adaptive unknown probability density function predictors. Theoretically, show proposed estimator has same convergence rate as full-basis roughly O[n2d/{(pr+1)(d +2)}] where p ∈[1, 2] and r ≈ 4 some constants depend type spline. Numerical studies various synthetic datasets demonstrate superior comparison with mainstream competitors.